Taylor has $32000 a part of which he invested at 5% and the remainder at 3%. His annual return on each investment is the same. At what rate would he have to invest all her money to get the same interest?

Taylor have to invest the total money at 3.75%

Step-by-step explanation:

Let the part of money invested at 5% be 'a' and the part of money invested at 3% be (32000-a).

To find (a) :

The annual income for both the 5% and 3% investment is equal.

Interest= (amount x rate of interest x time) /100

Interest for 5% rate on investment

Interest = (a x 5 x 1) /100

Interest for 3% rate on investment

Interest = [(32000-a) x 3 x 1]/100

Both the interests are equal so equate both the equations.

(a x 5 x 1) /100 = [(32000-a) x 3 x 1] /100

5a = (32000-a) 3

5a = 96000-3a

8a = 96000

a = 96000/8

a = 12000

32000-a = 32000-12000

= 20000

The amount invested at 5% is $12000 and invested $20000 at 3%

Interest = (12000 x 5 x 1) /100

= 60000/100

= $600

Interest = (20000 x 3 x 1) /100

= 60000/100

= $600

Total interest = $1200

To find the rate at which the total money is to be invested to get the same annual income.

1200 = (32000 x rate x 1) /100

1200 x 100 = 32000 x rate x 1

120000 = 32000 x rate

120000/32000 = rate

Rate = 3.75%

Taylor have to invest the total money at 3.75% to get the same annual income

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.